which is relative Riemann-Roch theorem. It agrees with ([1]}) except that here we state it uniformly for all one-dimensional global fields. It is also worth noticing that the formula also agrees with what we would obtain in [2]} using the relative normalisation of the Haar measure. Indeed, the Riemann-Roch statement has the following form
\(\frac{1}{|\alpha |}\sum \limits _{u \in K} \hat{f}(u/\alpha )=\sum \limits _{u\in K} f(\alpha u)\) 
